Four different devices beep after every half hour, 60 min, 1 and half hours, and 135 min respectively. All the devices beeped together at 12 noon. They will beep together again at:Options :A] 12 midnightB] 6 AMC] 9 PMD] 7:30 AM
Question
Four different devices beep after every half hour, 60 min, 1 and half hours, and 135 min respectively. All the devices beeped together at 12 noon. They will beep together again at:Options :A] 12 midnightB] 6 AMC] 9 PMD] 7:30 AM
Solution 1
To solve this problem, we need to find the least common multiple (LCM) of the four time intervals. The time intervals are 30 minutes, 60 minutes, 90 minutes, and 135 minutes.
First, convert all the time intervals into minutes:
- 30 minutes = 30
- 60 minutes = 60
- 1 and half hours = 90 minutes
- 135 minutes = 135
Now, find the LCM of 30, 60, 90, and 135. The LCM of these numbers is 540 minutes.
540 minutes is equal to 9 hours.
So, if all the devices beeped together at 12 noon, they will beep together again 9 hours later, which is 9 PM.
So, the answer is C] 9 PM.
Solution 2
To solve this problem, we need to find the least common multiple (LCM) of the four time intervals.
First, convert all the time intervals into minutes:
- Half an hour is 30 minutes
- 60 minutes is already in minutes
- 1 and a half hours is 90 minutes
- 135 minutes is already in minutes
So, we need to find the LCM of 30, 60, 90, and 135.
The LCM of these numbers is 540 minutes.
540 minutes is equal to 9 hours.
So, if all the devices beeped together at 12 noon, they will beep together again 9 hours later, which is 9 PM.
So, the answer is C] 9 PM.
Solution 3
To solve this problem, we need to find the least common multiple (LCM) of the four time intervals.
First, we need to convert all the time intervals into the same unit. In this case, we'll use minutes:
- Half an hour is 30 minutes.
- 60 minutes is already in minutes.
- 1 and a half hours is 90 minutes.
- 135 minutes is already in minutes.
So, we need to find the LCM of 30, 60, 90, and 135 minutes.
The LCM of these numbers is 540 minutes.
540 minutes is equal to 9 hours.
So, if all the devices beeped together at 12 noon, they will beep together again 9 hours later, which is 9 PM.
Therefore, the answer is C] 9 PM.
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